We suggest coherent switching of canted antiferromagnetic (AFM) spins using spin-orbit torque (SOT) in small magnet. The magnetic system of orthoferrite features biaxial easy anisotropy and the Dzyaloshinskii Moriya interaction, which is perpendicular to the easy axes and therefore creates weak magnetization (m). A damping-like component of the SOT induces Neel reorientation along one of the easy axes and then exerts torque on m, leading to tilting of the Neel order l. The torque on the magnetization becomes stronger due to coupling with the induced Oersted field or the field-like component of the SOT, enhancing the tilting of l. Therefore, l is found to experience deterministic switching after the SOT is turned off. Based upon both numerical and analytical analysis of the coherent switching, XOR logic gates are also found to be implemented in a single magnetic layer. In addition, we investigate how magnetic parameters affect the critical reorientation angle and current density in a simple layered structure of platinum and a canted AFM. Our findings are expected to provide an alternative spin-switching mechanism for ultrafast applications such as spin logic and electronic devices.
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